TSKS01 Digital Communication Lecture 1

Transcription

1 TSKS01 Digital Communication Lecture 1 Introduction, Repetition, Channels as Filters, Complex-baseband representation Emil Björnson Department of Electrical Engineering (ISY) Division of Communication Systems

2 Emil Björnson Course Director TSKS01 Digital Communication TSKS12 Multiple Antenna Communication Associate Professor (Biträdande professor) Docent in Communication Systems, PhD in Telecommunications Coordinator of and Master programme in Communication Systems Master profile in Communication Systems Researcher on 5G communications (e.g., multiple antenna communications). Theoretical research and inventor TSKS01 Digital Communication - Lecture 1 2

3 TSKS01 Digital Communication - Formalities Information: and LISAM Lecturer & examiner: Emil Björnson, emil.bjornson@liu.se Tutorials: Kamil Senel, kamil.senel@liu.se Teaching activities: 12 lectures, 12 tutorials, lab exercises Examination: Laboratory exercises (1 hp): New lab: deep learning vs. digital communication More details in HT2 Written exam (5 hp): 1 simple task (basics) Min: 50% 2 questions (5 points each) Min: 3p 4 problems (5 points each) Min: 6p Pass: 14 points from questions & problems TSKS01 Digital Communication - Lecture 1 3

4 Course Aims After passing the course, the student should be able to reliably perform standard calculations regarding digital modulation and binary (linear) codes for error control coding. (basics) should be able, to some extent, to perform calculations for solutions to practical engineering problems that arise in communication (primarily questions) be able to, with some precision, analyze and compare various choices of digital modulation methods and coding methods in terms of error probabilities, minimum distances, throughput, and related concepts. (problems) be able, to some extent, to implement and evaluate communication systems of the kinds treated in the course. (laboratory exercises) TSKS01 Digital Communication - Lecture 1 4

5 Course Book Introduction to Digital Communication New edition for 2018, A1758, SEK 272 Contains theory and tutorial problems 274 pages dedicated to this course Available for purchase in Building A, LiU Service Center, entrance 19C Older editions Version from 2017 (two books) can be used, but is not recommended. Follow last year s course website for list of tutorial problems TSKS01 Digital Communication - Lecture 1 5

6 Outline Introduction, lecture plan Briefly: Signals and systems, Fourier transforms, probability theory Complex baseband modeling Basic communication example Stochastic processes important for noise modeling Popular science videos on Youtube: Communication Systems, Linköping University, LIU TSKS01 Digital Communication - Lecture 1 6

7 What is Communication? Information transfer n n n Classic technology Newspapers, books Telegraph Radio and TV broadcast Modern digital technology n n n CD, DVD, Blu-ray Optical fibres, network cables Wireless (4G, WiFi) TSKS01 Digital Communication - Lecture 1 7

8 Why Digital Communication? 1. Efficient Source Description Information has a built-in redundancy (e.g., text, images, sound) Compression: Represent information with minimal number of bits Sequence of bits: 0 and bits represent 2 "## # different messages 2. Efficient Transmission Nyquist-Shannon Sampling Theorem:, Hz signal 2, samples per s Sequence of bits is used to select these samples 3. Guaranteed Quality Protect signals against errors: All or nothing is received TSKS01 Digital Communication - Lecture 1 8

9 One-way Digital Communication System Sender Error control Digital to analog Medium Source Channel encoder Modulator Channel coding Digital modulation Analog channel Destination (Sink) Channel decoder Demodulator Error correction Analog to digital Detector TSKS01 Digital Communication - Lecture 1 9

10 Digital Communication: An Exponential Story Overall IP traffic Digital Communication Devices are Everywhere PCs, tablets, phones, machine-to-machine, TVs, etc. Total internet traffic: 23% growth/year Number of devices: 12% growth/year How can we sustain this exponential growth? Source: Cisco VNI Global IP Traffic Forecast, TSKS01 Digital Communication - Lecture 1 10

11 Information-Bearing Signals Example: Mobile communication Analog electromagnetic signaling Bandwidth! Hz Sample principle in copper cables, optical fibers, etc. Nyquist Shannon Sampling Theorem Signal is determined by 2! real samples/second (or! complex samples) Information-bearing signals Select the samples in a particular way à Represent digital information Spectral efficiency: Number of bits transferred per sample [bit/s/hz] TSKS01 Digital Communication - Lecture 1 11

12 Designing Efficient Communication Systems Performance metric: Bit rate [bit/s] Bit rate [bit/s] = Bandwidth Hz. Spectral ef4iciency [bit/s/hz] How do we increase the bit rate? 1. Use more bandwidth 2. Increase spectral efficiency Wired: Use cable that handles wider bandwidths Wireless: Buy more spectrum This course deals with spectral efficiency! Each sample represents more bits More sensitive to disturbances Improve signal by smart modulation and demodulation Protect against bit errors with coding TSKS01 Digital Communication - Lecture 1 12

13 Preliminary Lecture Plan HT1: Introduction, repetition, noise modeling (Lecture 1) Basic digital modulation (Lectures 2-3) Detection in AWGN channels, modulation schemes (Lectures 3-5) Detection in dispersive channels (Lectures 6-7) HT2: Error control coding (Lectures 8-10) Practical aspects (e.g., synchronization), lab intro (Lecture 11) Link adaptation (Lecture 12) TSKS01 Digital Communication - Lecture 1 13

14 What You are Expected to Know Signals and systems Typical signals, LTI systems, impulse response Fourier transform Applied to signals and systems Probability theory Stochastic variables, mean value, variance, etc. Repetition videos in Lisam TSKS01 Digital Communication - Lecture 1 14

15 Repetition: Signals and Systems Signals: Systems: Voltages, currents, or other measurements Manipulate/filter signals!(#) System %(#) Complex exponential: & '()*+ = cos 212# + 4 sin(212#) Unit step: 7(#) = 8 0, # < 0 1, # > 0 Unit impulse: Property: A! # > # C D# =!(C) + 7 # > E DE TSKS01 Digital Communication - Lecture 1 15

16 Properties of systems General case: &(#) Energy-free system '(#) Energy-free system: No transients, constant input à constant output Impulse response: Energy-free!(#) h(#) system Linear time-invariant (LTI) system Linear: Output is scaled, time-delayed versions of input Time-invariant: Always reacts in the same way TSKS01 Digital Communication - Lecture 1 16

17 Convolution and Output of System Definition: The convolution of the signals!(#) and %(#) is denoted by (! %)(#) and defined as *! % # = ( )*! + % # Commutative operation:! % # = %! #. Theorem: Let /(#) be the input to an energy-free LTI system with impulse response h(#), then the output of the system is 1 # = / h #. /(#) h # 1 # = (/ h)(#) TSKS01 Digital Communication - Lecture 1 17

18 Example: Communication Channel is an LTI Filter Time delay: & ' Time delay: & * Time delay: & ) Time delay: &, Impulse response: h " = $ " & ' + $ " & ) + $ " & * + $(" &, ) Only time-invariant for a limited time period (coherence time) TSKS01 Digital Communication - Lecture 1 18

19 Fourier Transform Fourier transform Fourier transform:! " = F %(') = *+ + % ', *-./01 2' Exists if *+ + % ' 2' < Inverse transform: F *6!(") = *+ +! ", -./01 2" Common terminology Amplitude spectrum:! " Phase spectrum: arg!(") TSKS01 Digital Communication - Repetition

20 Fourier Transform Examples Cosine:! " = cos 2() * " + ) = ) ) * () + ) *) Sine:! " = sin 2() * " + ) = ) ) * () + ) *) Rectangle pulse:! " = 5 " + 1 5(" 1) + ) = sinc ) = sin () () TSKS01 Digital Communication - Repetition

21 Example: Two Baseband Signals Consider two real-valued baseband signals! " #,! % # Bandwidth & ' Fourier transforms satisfy ( " & = ( " &, ( % & = ( % ( &) TSKS01 Digital Communication - Lecture 1 21

22 Modulation from Baseband to Passband We need to communicate around the frequency! " Create a passband signal from # $ %, # ' % : # % = # $ % 2 cos 2-! " % # ' % 2 sin 2-! " % TSKS01 Digital Communication - Lecture 1 22

23 Recall: Fourier Transform Recall: F " # = %(') F cos 2-'. # = ' ' (' + '.) Consequence: F " # cos(2-'. #) = 1 2 % ' ' %(' + '.) Baseband: " #, %(') Passband: " # cos 2-'. #, 3 '. 5 6 % ' ' %(' + '.) ' ' '. '. 0 ' TSKS01 Digital Communication - Repetition

24 Demodulation from Passband to Baseband Upper part: 2 cos 2%& ' ( ) ( = ) + ( 2 cos, 2%& ' ( ). ( 2 sin 2%& ' ( cos 2%& ' ( = ) + ( + ) + ( cos 4%& ' ( ). ( sin 4%& ' ( Centered around frequency 2& ' ; easy to cancel with low-pass filter TSKS01 Digital Communication - Lecture 1 24

25 Complex Baseband Representation Define a complex baseband signal instead: " # = " % # + '" ( (#) with Fourier transform +, - =, % - + ', ( (-) We can obtain passband signal as " # =./ 2" # / = 1 2 " # / " # / = " % # 2 cos 2=- > # " ( # 2 sin 2=- > # Hence:, - = B 2 +, - - > + +, > TSKS01 Digital Communication - Lecture 1 25

26 Spectrum of complex baseband signal 1 2!" # = " % # + '" ( # = )* " % (#)./ " ( # +'./ " % # + )* " ( # Spectrum of passband signal 1 2 " # = 1 2!" # # 5 +!" # + # TSKS01 Digital Communication - Lecture 1 26

27 Probability, Stochastic Variable, and Events Total probability: Pr Ω $ = 1 Probability of event ': Pr{'} [0,1] Sample space: Ω 4 Stochastic variable Joint probability: Pr{', /} Conditional probability: Pr ' / = 01{2,3} 01{3} 5 4 Event ' Event / Measureable sample space: Ω $ = 5 4 : for some 4 Ω TSKS01 Digital Communication - Lecture 1 27

28 Probability Theory Stochastic variable!, taking realizations " Probability distribution function: #! (") = Pr{! "} [0,1] Probability density function (PDF): 2! (") = 3 3" #!(") Properties: #! (") is non-decreasing, #! (") 0 and 2! (") 0 for all ", (") 3" = 1, TSKS01 Digital Communication - Lecture 1 28

29 Expectation and Variance Expectation (mean):! " = $ & %& '( ) ' *' For discrete variables:! " = + ', Pr{" = ', }, Quadratic mean (power):! " 1 = $ & %& ' 1 ( ) ' *' Variance Var " =! "! " 1 =! " 1! " 1 Common notation: 5 ) =! ", 5 6 =! ) = Var " 8 ) is called the standard deviation TSKS01 Digital Communication - Lecture 1 29

30 Gaussian/Normal Distribution,!(#, % & ) Probability density ( ) * = 1 % 2. / &4 3 Mean: # Variance: % & 1 Probability distribution 5 ) * = () 07 * 8* is complicated 9-function 7 ; 9 * = 1 5 ) * = 1 &< /0=3 3 8> for!(0,1) Can be computed from table TSKS01 Digital Communication - Lecture 1 30

31 Example of the! Function!(1.96) / TSKS01 Digital Communication - Lecture 1 31

32 Bayes Theorem Thomas Bayes Joint and conditional probability: Pr{$ = &, ( = )} = Pr $ = & ( = ) Pr{( = )} = Pr{( = ) $ = &} Pr{$ = &}, -,. &, ) =, -. & ),. ) =,. - ) &, - & Bayes theorem (discrete): Pr{$ = & ( = )} = /0{.12-13} /0{.12} Pr{$ = &} (continuous):, -. & ) = , - & ($ discrete, ( cont.): Pr{$ = & ( = )} = Pr{$ = &} TSKS01 Digital Communication - Lecture 1 32 Image from:

33 Example: Additive Noise Channel -!, + Detector.! Input:! 1, +1 with Pr! = +1 = Pr! = 1 = 1/2 Output:, =! (/) 1/2 - is a continuous stochastic variable / How should we best detect! from,? TSKS01 Digital Communication - Lecture 1 33

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